A note on a combinatorial interpretation of the e-coefficients of the chromatic symmetric function
| dc.creator | Chow, Timothy Y. | |
| dc.date | 1997-12-04 | |
| dc.date | 2002-08-16 | |
| dc.date.accessioned | 2026-07-07T05:23:22Z | |
| dc.date.available | 2026-07-07T05:23:22Z | |
| dc.description | Stanley has studied a symmetric function generalization X_G of the chromatic polynomial of a graph G. The innocent-looking Stanley-Stembridge Poset Chain Conjecture states that the expansion of X_G in terms of elementary symmetric functions has nonnegative coefficients if G is a clawfree incomparability graph. Here we give a combinatorial interpretation of these coefficients by combining Gasharov's work on the conjecture with Egecioglu and Remmel's combinatorial interpretation of the inverse Kostka matrix. This gives a new proof of a partial nonnegativity result of Stanley. As an interesting byproduct we derive a previously unnoticed result relating acyclic orientations to P-tableaux. | |
| dc.description | Minor error corrected | |
| dc.identifier | https://arxiv.org/abs/math/9712230 | |
| dc.identifier | http://arxiv.org/abs/math/9712230 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76411 | |
| dc.subject | Combinatorics | |
| dc.subject | 05 | |
| dc.title | A note on a combinatorial interpretation of the e-coefficients of the chromatic symmetric function | |
| dc.type | text |